1. If the algebraic expression is meaningful, then the value range of x is ().
a . x≥0 b . x≠ 1 c . x & gt； 0 d x ≥ 0 and x≠ 1
2. In the following groups, triangles with side lengths A, B and C are not right triangles ().
A b
C D
As shown in the figure, there are three squares on the straight line. If the areas are 5 and 1 1 respectively, the area is ().
16 D.55
4. As shown in the figure, in the parallelogram ABCD, the following conclusion is wrong ().
A.∠ 1 =∠2b .∠bad =∠BCD c . ab = CD d . ac⊥bd
5. As shown in the figure, in the parallelogram ABCD, diagonal AC and BD intersect at point O, point E and point F are the midpoint of the sides of AD and AB respectively, and EF and AC intersect at point H, so the value is ().
A. BC 1 year
6. The image of is as shown in the figure. When is, the value range of is ()
A.B. C. D。
7. In physical education class, a group of 20 people played a football match, and each person was fined five times. It is known that the total number of goals in a certain group is 49. The goals are recorded in the table below, in which X scored two goals and Y scored three goals. If (x, y) happens to be the coordinates of the intersection of two straight lines, then the analytical formula of these two straight lines is
Target quantity 0 1 2 3 4 5
Number 1 5 x y 3 2
A.y=x+9 and y= x+ B. y=-x+9 and y=x+
C.y=-x+9 and y =-x+d. Y = x+9 and y =-x+
8. It is known that the image of linear function y=kx+b(k and b are constants, k≠0) passes through point A (0, ﹣2) and point B (1, 0), then k=, b=
9. It is known that in Δ ABC, AB = 4, AC = 3 and BC =, then the area of Δ ABC is ().
A.6 B.5 C. 1.5 D.2
10. As shown in the figure, it is known that a straight line passes through point A (0,2) and point B (1 0). Translate this line to the left, and intersect with point C and point D on the X axis and Y axis respectively. If DB=DC, the resolution function of straight CD is.
1 1. In quadrilateral ABCD, diagonal AC and BD intersect at point O, and the following conditions cannot determine that this quadrilateral is a parallelogram ().
A.AB∨DC, AD∨ BC B. AB=DC, AD = BC C. AO=CO, BO = DO d. AB∨DC, AD = BC.
12. There is a right-angled triangular paper, as shown in figure 1, with two right-angled sides AC = 6 cm and BC = 8 cm. Now fold the right angle AC along the straight line AD, so that it falls on the hypotenuse AB and coincides with AE, and CD is equal to ().
A.2cm, B.3cm, C.4cm, D.5cm
Second, fill in the blanks:
13. Calculation:
14. If known, then = _ _ _ _ _ _.
15. If the image of the linear function y=kx+ 1(k is a constant, k≠0) passes through the first, second and third quadrants, the value range of is.
16. If a sample is 3,-1, a, 1,-3,3. Their average is a, so the variance of this sample is.
17. In quadrilateral ABCD, diagonal AC and BD intersect at point O, and the following four conditions are given:
(1) AD ∨ BC; ②AD = BC； ③OA = OC； (4) Choose two conditions from OB = OD, and there are several ways to make the quadrilateral ABCD a parallelogram.
18. Figure 3 is the emblem of the 24th International Congress of Mathematicians held in Beijing in August 2002. It is a big square consisting of four congruent right-angled triangles and a small square in the middle. If the area of a big square is 13, the area of a small square is 1, the long right side of a right triangle is A, and the short right side is B, then a +b B.
19. If the range of a set of data 1, 2, 3 and x is 6, then the value of x is.
20. As shown in the figure on the right below, at Rt△ABC, AC=5, BC= 12, three semicircles are made upward with their three sides as diameters, and the area of the shaded part is.
Third, answer questions:
2 1.(6 points) Calculation: (2) 2012 (2+) 2013-2-() 0.
2 2.(8 points) As shown in the figure, E and F are two points on the diagonal AC of the quadrilateral ABCD, AF=CE, DF=BE, DF∨BE.
Verification: (1) △ AFD △ CEB;
(2) The quadrilateral ABCD is a parallelogram.
23.(20 13? Mudanjiang) two cars, A and B, set off from City A to City B two hours in advance. A stays for a period of time after arriving in city B, and returns immediately after arriving in city B. The round-trip speed of both cars is 40km/h, and the round-trip speed of both cars is 20 km/h. The following figure shows the function image between the distance S (km) of city A and the driving time T (h). Please answer the following questions with pictures.
(1) The distance between A and B is kilometers. After A arrives at B, B arrives at B in an hour;
(2) Find the functional relationship between the distance s (km) and the time t (hours) when the A car returns, and write the range of the independent variable t;
(3) Please write directly that the distance between a car and b car is 15km after several hours.
2 4.(8 points) As shown in the figure: In a square ABCD, e is the midpoint of AB, and f is the upper point of AD. Find the degree of ∠FEC.
2 5. As shown in the figure, there are two villages A and B on the same side of the railway L. It is known that the distance from village A to L is AC= 15km, and the distance from village B to L is Bo = 10 km, and CD=25km. Now it is necessary to build a local product purchasing station E on the railway L, so that the distance from village A and village B to station E is equal. (1) Use a ruler. (2) Find the length of CE
26.(20 13? There are 10 workers in a product workshop in Baotou. It is known that each worker can produce 12 pieces of Class A products or 10 pieces of Class B products every day, and each piece of Class A products can earn 100 yuan, and each piece of Class B products can earn 180 yuan.
(1) Please write down the functional relationship between the daily profit y (yuan) and x (person) of this workshop;
(2) If the daily profit of this workshop is 14400 yuan, how many workers will be sent to produce Type A products?
(3) If the daily profit of this workshop is not less than 15600 yuan, how many workers do you think it is appropriate to send at least to produce the second product?
27. As shown in the figure, △ABC and △DEF are equilateral triangles with a side length of 6㎝, and A, D, B and F are on the same straight line, connecting CD and BF.
(1). Quadrilateral BCDE is a parallelogram.
(2). If AD=2㎝,△ABC moves in the direction of AF at a speed of 1㎝ per second, and let △ABC move.
The time is t seconds. (a) What is the value of t, and the parallelogram BCDE is a diamond? Please explain your reasons.
Is it possible for parallelogram BCDE to be rectangular? If possible, find out the value of t and find out
The area of a rectangle. If not, please explain why.
28. As shown in the figure, in Rt△ABC, ∠ c = 90, make an equilateral triangle ACD with AC as one side and point E as the midpoint of AB, connecting de.
(1) Prove de ∑ CB;
(2) When discussing the quantitative relationship between AC and AB, the quadrilateral DCBE is a parallelogram. In ABCD, point O is the intersection of AC and BD, and the straight line passing through point O intersects with the extension lines of BA and DC at points E and F respectively.
(1) Verification: △ AOE △ COF;
(2) Please connect EC and AF, so if EF and AC meet any conditions, the quadrilateral AECF is a rectangle, and explain the reasons.
28.( 1) Proof: Link CE.
Point e is the midpoint of hypotenuse AB of Rt△ACB,
∴CE=AB=AE.
△ ACD is an equilateral triangle,
∴AD=CD.
In ade and CDE,
∴△ADE≌△CDE(SSS)，
∴∠ADE=∠CDE=30。
∫∠DCB = 150，
∴∠EDC+∠DCB= 180。
∴DE∥CB.
(2) solution: ∫≈DCB = 150, if the quadrangle DCBE is a parallelogram, then DC∨BE, ∠ DCB+∠ B = 180.
∴∠B=30。
In Rt△ACB, sinB=, sin30 =, AC= or AB=2AC.
When AC= or AB=2AC, the quadrangle DCBE is a parallelogram.
This question mainly examines the determination of parallel lines, congruent triangles and parallelogram. The key is to master the properties of right triangle and equilateral triangle.
29.( 1) Prove that the ∵ quadrilateral ABCD is a parallelogram.
∴AO=OC,AB∥CD.
∴∠e =∞∠f and ∠AOE =∞cof.
∴△aoe≌△cof(asa)；
(2) When EC and AF are connected, if EF and AC satisfy EF=AC, the quadrilateral AECF is rectangular.
The reason for this is the following：
According to (1), △ AOE △ COF
∴OE=OF，
AO = CO，
∴ Quadrilateral AECF is a parallelogram,
EF = AC，
∴ Quadrilateral AECF is a rectangle.